The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
| b, -a, -c | -x, -y, -z | { -1 ‖ -4+001 | 0 } |
| -b, a, -c | -x, -y, -z | { -1 ‖ -4-001 | 0 } |
| a+1/2, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ -4+001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ -4-001 | 1/2 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| b, -a, -c | x, -y, -z | { 2 ‖ -4+001 | 0 } |
| -b, a, -c | x, -y, -z | { 2 ‖ -4-001 | 0 } |
| a+1/2, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4+001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4-001 | 1/2 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2b | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
| 2c | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (0,1/2,1/4 | 0,0,0) |
| 2d | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (0,1/2,3/4 | 0,0,0) |
| 4e | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
| 4f | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
| 8g | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $\ce{^{-1}{-4}}\ce{^{\infty m}{1}} $ |
| M:(1,1,1) | $\ce{^{-1}{-4}}\ce{^{\infty m}{1}} $ |
| P:(1/2,1/2,1/2) | $\ce{^{2}{-4}}\ce{^{\infty}{1}} $ |
| X:(1/2,1/2,0) | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| N:(1/2,0,1/2) | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{-1}{-4}}\ce{^{\infty}{1}} $ |
| W:(1/2,1/2,w) | $\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Y:(u,1-u,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Δ:(u,u,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| A:(u,u,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| M:(0,0,-1) | Y:(0,1,0) | $(M)Y_{1}^{S}(2) $ | |
| N:(-1/2,1,-1/2) | L:(1/2,1/2,1/2) | $2(N)L_{1}^{S}(1)$ | Spin Splitting |
| P:(-1/2,1/2,-1/2) | U:(0,1/2,1/2) | $(P)U_{1}^{S}(2) $ | |
| X:(-1/2,1/2,-1) | M:(0,1,1/2) | $2(X)M_{1}^{S}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,-w,-u) | $2(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,-w,-u) | $2(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-u) | $2(C)B_{1}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $2(Δ)B_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,-1/2,-1/2) | $2(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,-u) | $2(Σ)B_{1}^{S}(1)$ | Spin Splitting |
| W:(-1/2,1/2,-1+w) | U:(0,1-w,1/2) | $2(W)U_{1}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-u) | $2(Y)B_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,-w,-u) | $2GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| M:(0,0,-1) | Y:(0,1,0) | $(M)Y_{1}^{S}(2) $ | |
| N:(-1/2,1,-1/2) | L:(1/2,1/2,1/2) | $2(N)L_{1}^{S}(1)$ | Spin Splitting |
| P:(-1/2,1/2,-1/2) | U:(0,1/2,1/2) | $(P)U_{2}^{S}(2) $ | |
| X:(-1/2,1/2,-1) | M:(0,1,1/2) | $2(X)M_{2}^{S}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,-w,-u) | $2(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,-w,-u) | $2(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-u) | $2(C)B_{1}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $2(Δ)B_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,-1/2,-1/2) | $2(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,-u) | $2(Σ)B_{1}^{S}(1)$ | Spin Splitting |
| W:(-1/2,1/2,-1+w) | U:(0,1-w,1/2) | $2(W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-u) | $2(Y)B_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,-w,-u) | $2GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
| M:(0,0,-1) | Y:(0,1,0) | $(M)Y_{1}^{S}(2)⊕(M)Y_{2}^{S}(2) $ | |
| N:(-1/2,1,-1/2) | L:(1/2,1/2,1/2) | $4(N)L_{1}^{S}(1)$ | Spin Splitting |
| P:(-1/2,1/2,-1/2) | U:(0,1/2,1/2) | $(P)U_{1}^{S}(2)⊕(P)U_{2}^{S}(2) $ | |
| X:(-1/2,1/2,-1) | M:(0,1,1/2) | $2(X)M_{1}^{S}(1)⊕2(X)M_{2}^{S}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,-w,-u) | $4(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,-w,-u) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-u) | $4(C)B_{1}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $4(Δ)B_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,-1/2,-1/2) | $4(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,-u) | $4(Σ)B_{1}^{S}(1)$ | Spin Splitting |
| W:(-1/2,1/2,-1+w) | U:(0,1-w,1/2) | $2(W)U_{1}^{S}(1)⊕2(W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-u) | $4(Y)B_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,-w,-u) | $4GP_{1}^{S}(1)$ | Spin Splitting |